Abstract: Neural QCFG is a grammar-based sequence-to-sequence model with strong inductive biases on hierarchical structures. It excels in interpretability and generalization but suffers from expensive inference. In this paper, we study two low-rank variants of Neural QCFG for faster inference with different trade-offs between efficiency and expressiveness. Furthermore, utilizing the symbolic interface provided by the grammar, we introduce two soft constraints over tree hierarchy and source coverage. We experiment with various datasets and find that our models outperform vanilla Neural QCFG in most settings.